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Indeterminate Forms Questions, Exams of Mathematics

Chaudhary Charan Singh UniversityMathematics

Indeterminate Forms Questions for exam

Typology: Exams

2016/2017

Uploaded on 06/16/2017

vivekgarg284
vivekgarg284 🇮🇳

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bg1
Indeterminate Forms
1
Some Important results:
1.

123
1 x 1 x x x .......
 2.

234
xxx
Log 1 x x .......
234

3.
357
xxx
Sinx x .......
357
 4.
246
xxx
Cosx 1 .......
246

5.
35
x2x
Tanx x .......
315
 6 .
234
xxxx
e 1 x .......
234

7.
2
1xx11x
(1 x) e 1 .......
224




8. b
a
log(ab) log a l ogb; log(a / b) log a l og b; log a b loga; log a 1 
9.

1x
x0
Lim 1 x e

; log1 0; log e 1; log ; log0 ; e ; e 0;


1.
2
5
x0
1
Sinx x x
6
Lim x

2. 2
x0
xCosx Log(1 x)
Lim x

3.
12
3
x2
x0
xTanx
Lim
(e 1)
4.
1x
x0
(1 x) e
Lim x

5. x0
Sinx
Lim x
6.
x
x0
e1
Lim x
7. 2
x0
1Cosx
Lim x
8.
xx
x0
ab
Lim x
9. 2
x
x0
xe Log(1 x)
Lim x

10. 3
x0
xSinx
Lim Tan x
11. x1
logx
Lim x1
12. 2
x0
Tanx x
Lim xTanx
13.
xSinx
x0
ee
Lim xSinx
14.
1x
2
x0
1
(1 x) e ex
2
Lim x

15.
12
6
x0
SinxSin x x
Lim x
16.
1
2
x0
SinxSin x
Lim x
17.
22
4
x0
Sin x x
Lim x
18.
x
x0
1x
eLoge
Lim Tanx x



19.
x2
Cosx
Lim
x2





20. x0
logx
Lim Cotx
21. x0
logSin2x
Lim logSinx
22.
2
x0
log log(1 x )
Lim log logCosx
23.
x2
1
Lim Secx 1Sinx



24.
x0
Lim x lo gSinx
25. x0
Cotx
Lim(Cosx)
26.
x
x
a
Lim 1 x




27.
2
x0
Cot x
Lim(Cosx)
28. 2
2
x0
11
Lim xSinx



29. 2
x0
1Log(1x)
Lim xx



30.
1x
x0
Sinx
Lim x



31.
2
1x
x0
Tanx
Lim x



32. x0
1
Cotx x
Lim x





33. x0
Co sec x Cotx
Lim x



34.

x0
Lim Sinx logx
35.

x0
Lim x logx
36.

x2
Lim Secx Tanx
37. x
x0
11
Lim e1x



pf3
pf4
pf5

Partial preview of the text

Download Indeterminate Forms Questions and more Exams Mathematics in PDF only on Docsity!

Some Important results :

(^1 2 ) 1 x 1 x x x .......

2 3 4 x x x Log 1 x x ....... 2 3 4

3 5 7 x x x Sinx x ....... 3 5 7

2 4 6 x x x Cosx 1 ....... 2 4 6

3 5 x 2x Tanx x ....... 3 15

2 3 4 x x^ x^ x e 1 x ....... 2 3 4

1 2 x x^ 11x (1 x) e 1 ....... 2 24

b a

log(ab)  log a  l og b; log(a / b)  log a  l og b; log a  b loga; log a  1

1 x

x 0

Lim 1 x e 

  ; log1 0; log e 1; log ; log0 ; e ; e 0;

           

2

x 0 5

Sinx x x 6 Lim  x

x 0 2

xCosx Log(1 x) Lim  x

1 2

3 x (^0) x (^2)

x Tanx Lim

(e 1)

 

1 x

x 0

(1 x) e Lim  x

x 0

Sinx Lim  x

x

x 0

e 1 Lim  x

x 0 2

1 Cosx Lim  x

x x

x 0

a b Lim  x

2

x

x 0

xe Log(1 x) Lim  x

3 x 0

x Sinx Lim  Tan x

x 1

logx Lim  (^) x  1

2 x 0

Tanx x Lim  x Tanx

x Sinx

x 0

e e Lim  x Sinx

1 x

x 0 2

(1 x) e ex 2 Lim  x

1 2

6 x 0

SinxSin x x Lim x

1

2 x 0

SinxSin x Lim x

2 2

x 0 4

Sin x x Lim  x

x

x 0

1 x e Log e Lim  Tanx x

x (^2)

Cosx Lim

x 2

^ 

x 0

logx Lim  Cotx

x 0

logSin2x Lim  logSinx

2

x 0

log log(1 x ) Lim  log logCosx

x (^2)

Lim Secx  1 Sinx

x 0

Lim x logSinx 

x 0

Cotx Lim(Cosx) 

x

x

a Lim 1  x

2

x 0

Cot x Lim(Cosx) 

  1. (^2) 2 x 0

Lim  x Sin x

  1. (^2) x 0

1 Log(1 x) Lim  x x

1 x

x 0

Sinx Lim  x

(^12) x

x 0

Tanx Lim  x

x 0

Cotx x Lim  x

x (^0)

Co sec x Cotx Lim  x

x (^0)

Lim Sinx logx 

x 0

Lim x logx 

x (^2)

Lim Secx Tanx ^ 

x x (^0)

Lim  e 1 x

  1. Find the values of ‘a’ and ‘b’ in order that 3 x 0

x(1 aCosx) bSinx

Lim

 x

may be equal to ‘1’.

  1. Find the values of ‘a’, ‘b’ and ‘c’ so that

x x

x 0

ae bCosx ce

Lim

xSinx

.

1 x

x 0

Lim(Cosx) 

1 (1 x)

x 0

Lim(x)

(^12) x

x (^0)

Sinx Lim  x

1 x

x

Logx Lim   x

1

1 x

x

Lim Tan x 2

 

1 Logx

x 0

Lim(Co sec x) 

x (^1)

x Lim(1 x)Tan  2

Tan 2x

4

x

Lim (Tanx) ^ 

x (^2)

Lim 1 Sinx Tanx ^ 

x

Lim xTan 1   x

3

2 x

x Logx Lim   1 x x